In polarized committees, majority voting disenfranchises the minority. Allowing voters to spend freely a fixed budget of votes over multiple issues restores some minority power. However, it also creates a complex strategic scenario: a hide-and-seek game between majority and minority voters that corresponds to a decentralized version of the Colonel Blotto game. We offer theoretical results and bring the game to the laboratory. The minority wins as frequently as theory predicts, despite subjects deviating from equilibrium strategies. Because subjects understand the logic of the game — minority voters must concentrate votes unpredictably — the exact choices are of secondary importance.